Train from Munich airport to Salzburg?

I don't believe so. You would take the Sbahn 8 to Munchen Ost, then change to the train to Salzburg. No advance reservation needed for the sbahn, but currently the Dbahn website is recommending seat reservations for the train due to high demand . If you wait to buy a ticket with a seat reservations, there's always a risk they might be sold out for the next train leaving. Or not.

You can buy a Bayern Ticket that will cover the cost out of a ticket vending machine at the airport. Leave after 9 am if a weekday. 25 EUR for the first person and 6 EUR for each additional person up to 5 traveling together. Take the S-8 to Munich Ost and change to a regional train to Salzburg. No IC, EC, or RJ trains. There are no reservations needed or available.

Definitely take the S8 to Ostbahnhof. There you could catch a Meridian (regional train), or you could take an IC or EC. The long distance trains are a few minutes faster, but more expensive. The Railjet costs more, and it takes longer because you have to go into the Hbf to get it. The Railjet does not stop at Ost (or anywhere else in Germany, for that matter).

BTW, the departure board at MUC shows the S1's destination as Ostbahnhof and the S8's as somewhere else (Herrsching, Weßling), but those are final destinations. The S1 goes around the west side of town and through the stem tunnel under Munich to Ost, it's final destination. The S8 goes around the east side of town, directly to Ost, then through Munich and on to its final destination well to the west, but it gets to Ostbahnhof quicker than does the S1.

Thanks for your help!

Nancy

Another good reason not to use the S1 is that, with the current construction work on the new tunnel under Munich, sometimes the S-Bahn can't run through the old tunnel and you have to be bused.